Piecewise Linear Analysis for Pseudo-elasticity of Shape Memory Alloy (SMA)

Based on the Brinson constitutive model of SMA, a piecewise linear model for the hysteresis loop of pseudo-elasticity is proposed and applied in the analysis of responses of an SMA-spring-mass system under initial velocity activation. The histories of displacement and velocity of the mass, and the response of stress of SMA are calculated with Brinson’s model and the piecewise linear model. The difference of results of the two models is not significant. The calculation with piecewise-linear model needs no iteration and is highly efficient.

STUDY OF CONSTITUTIVE RELATIONS FOR PSEUDO-ELASTICITY AND SHAPE MEMORY BEHAVIOR

Constitutive relations are given for the description of the deformation behavior of shape memory materials. The deformation is the superposition of the elastic, the thermal and the phase transformation deformation caused by the transformation from one to the other among the high temperature phase, the low temperature phase and the stress induced phase. The phase transformation is controlled by the driving force, i.e., the Gibbs energy difference between the phases.

A CONSTITUTIVE RELATION FOR PSEUDO-ELASTIC BEHAVIOUR IN SHAPE MEMORY ALLOYS

A constitutive relation to describe pseudo-elastic deformation in shape memory alloys is pres- ented in this paper. It is capable of describing deformation behaviour of polycrystalline materials under triaxial stress state as well as of monocrystalline materials under one-dimensional condition. Total strain rate is sup- posed to be composed of elastic strain rate and transformation strain rate. Deformation behaviour of Cu-Zn-Sn alloy and Ti-Ni alloy is simulated by use of the proposed constitutive relation. It is shown that simulated results are in a good agreement with experimental data.

Pseudo-elastic Hysteresis Damping Characteristics of SMA Hybrid Composite Lamina

The longitudinal mechanical behavior of shape memory alloy （SMA） composite lamina subjected to longitudinally strain or stress controlled cyclic loading is investigated. The SMA is under pseudoelastic condition and the fibers are embedded （bonded） to the host material. The influences of temperature, volume fraction of SMA and longitudinal modulus of the host material on the stress-strain relation and energy dissipation of the SMA hybrid composite lamina are discussed. The results indicate that the stress-strain curve of the lamina per cycle shows a hysteresis loop. The hysteresis damping decreases with increasing temperature and with decreasing volume fractions of SMA. In addition, the hysteresis damping is nearly independent of the longitudinal modulus of the host material under strain controlled loading. However, it depends dramatically on the longitudinal modulus of the host material under stress controlled loading, which shows the SMA composite lamina has high pseudo-elastic hysteresis damping when the longitudinal modulus of the host material is low.

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

A new finite strain elatoplastic J2-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate.In terms of certain single-variable shape functions representing uniaxial loading and unloading curves,explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys(SMAs)under multiple loading-unloading cycles.Numerical examples show that with only a single parameter of direct physical meaning for each cycle,accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.

Energy Dissipation Analysis of Bended SMA Bar in Isothermal State

The theory calculation formula is deduced about stress distribution in cross section and changes in Martensite percentages with the section height of random section shape bar under the action of the bending moment according to the Brinson's Constitutive Relation.The bar's energy dissipation capability under circulation of bending moment was analyzed and the calculation theory was set up. By using MATLAB program and the numerical calculation for uniform rectangle cross section bar, the relationships among the maximal stress and strain on cross section edge with bend load, the stress and Martensite percent's with cross section height, the energy dissipation capability with cross section height, and the energy dissipation capability with maximal strain on cross section edge are gained, also those curves are discused. It is put forward that the SMA material can be used for passive structure vibration control to dissipate energy of bend load.

ESTIMATION OF LOCAL HYSTERETIC PROPERTIES FOR SHAPE MEMORY ALLOYS

The applicability of shape memory alloys (SMAs) in structural dynamics,particularly as hysteretic damping elements, is limited by the difficulties in modelling theirdeformation characteristics. At typical engineering design levels of loading SMAs exhibitpseudo-elastic properties. A combined experimental and simulation approach suitable for thecharacterisation of novel smart devices based on the pseudo-elastic effect is described.